It is given that the data collected for a sample of 223 wells,
each well was classified according to well class and detectable
level of MTBE printout gives the number of wells in the sample with
a detectable level of MTBE for both the 120 public wells and the
103 private wells.

(a) We have to find the point estimate for the true proportion
of public wells with a detectable level of MTBE.

The point estimate of the proportion p is the sample
proportion, which is obtained from any sample drawn from
population, since sample proportion is an unbiased estimator of the
population proportion.

Thus, the sample proportion is,

Therefore, the point estimate for the true proportion of public
wells with a detectable level of MTBE is 0.40.

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Step 2 of 4

(b) We have to find the point estimate for the true proportion
of private wells with a detectable level of MTBE.

The point estimate of the proportion p is the sample
proportion, which is obtained from any sample drawn from
population, since sample proportion is an unbiased estimator of the
population proportion.

Thus, the sample proportion is,

Therefore, the point estimate for the true proportion of private
wells with a detectable level of MTBE is 0.21.

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Step 3 of 4

(c) We have to construct a 95% confidence interval estimate the
difference between the proportions of public and private wells with
a detectable level of MTBE.

The formula of the confidence interval for the two proportions
z-test is given below.

Confidence interval of two-proportion z-test is obtained,
by using Minitab software.

Instructions:

1. Click Stat, Basic Statistics, and 2
Proportions…

2. Select Summarized data….

3. Enter the values of Events, Trials for the
First and Second Samples in their corresponding
boxes…..

From the Minitab output, a 95% confidence interval for the
difference in means is shown below.

From the Minitab output, a 95 percent confidence interval
is.

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Step 4 of 4

(d) Based on the sample data, we can be 95% confident that the
difference in proportion of public and private wells with a
detectable level of MTBE is between 0.068 and 0.304. We used a
method to construct this estimate that captures the true difference
in proportions 95% of the time in repeated sampling.

The researchers can concluded that the true proportion of public
wells with a detectable level of MTBE is superior to the true
proportion of private wells with a detectable level of MTBE, since
the interval include only positive differences, we can be
reasonably confident that the true proportion of public wells with
a detectable level of MTBE is between 0.068 and 0.304 superior than
the true proportion of private wells with a detectable level of
MTBE.